Gravitational lensing in the peculiar 'magatama' galaxy

Apr 01, 2013

Figure 1: The imaging data taken with the Hubble Space Telescope (HST) of LAE 221724+001716 (left). The shape of LAE 221724+001716 in the HST image is peculiar and looks like a "magatama", an ancient Japanese amulet made of stone (right). (Credit: Ehime University)

(Phys.org) —In a course of studying young galaxies at a distance of 11.6 billion light years from Earth, a team of astronomers led by Professor Yoshiaki Taniguchi (Ehime University) noticed a strangely shaped galaxy that looks like a "magatama", an ancient, comma-shaped Japanese amulet made of stone (Figure 1). Subsequent research revealed that the magatama galaxy was actually an overlapping system of two young galaxies lying in an extremely close line of sight—an exceedingly rare occurrence among celestial objects. The small angular separation between the foreground and background galaxies gave the current team an opportunity to investigate the effect of gravitational lensing on the properties of the background galaxy. A member of the team, university student Yuya Nakahiro (Ehime University), calculated that the effect of gravitational amplification would be 20% at most. The foreground young galaxy is still forming, and the team concluded that the gravitational lensing effect from such a young galaxy does not affect the luminosity of its background galaxy.

The focus of the team's research was the young galaxy LAE 221724+001716, which lies about 11.6 billion light years from Earth. Team member Dr. Akio Inoue (Osaka Sangyo University) had made observations with the Subaru Telescope's prime focus camera (Suprime-Cam) and identified this galaxy as one of those emitting strong ultraviolet radiation that ionizes hydrogen atoms (Note); it is a Lyman-alpha emitter (LAE) and can provide important clues about the progenitors of Milky-Way type galaxies. Although he noticed that there was a separation between the galaxy itself and the emission point of ionizing radiation, he concluded that this galaxy did not include the effect of any foreground galaxies, given the negligible probability of an overlapping foreground galaxy with such a small separation from its background galaxy. However, another research team using Keck's Low Resolution Imaging Spectrometer (LRIS) found that the radiation, originally interpreted as ionizing radiation from LAE 221724+001716, came from a foreground galaxy located about 9.9 billion light years from Earth. Figure 2 shows the context for the images from the Subaru Telescope and HST in light of this revised interpretation.

Dr. Inoue expressed his surprise at the finding: "This result was very amazing to me, since this is the discovery of an extremely rare system." The finding sparked Professor Taniguchi's idea for the current research: "Soon after I knew this observational result, I became aware of the possibility that light from LAE 221724+001716 is gravitationally amplified by the foreground galaxy".

Figure 2: The shape and scale of the galaxies composing the magatama galaxy. a) Reference figure for the physical scales of the foreground and background galaxies. Using the physical scale of 10 kilo light years, the red lines represent the foreground galaxy while the blue lines represent the background galaxy. (Credit: Ehime University) b) The schematic view of LAE 221724+001716's shape (top) and imaging data taken with the Subaru Telescope (bottom left and middle) and the HST (bottom right). While both emissions detected in NB359 and NB497 images were originally thought to come from LAE 221724+001716, later observations revealed that most of the emission in NB359 comes from a foreground galaxy and that two distinct galaxies overlap and lie in an extremely close line of sight in the sky. 1 arcsecond (arcsec) is equal to 1/3600 of arc (part of a curve or circle). (Credit: Ehime University)

According to Einstein's Theory of Relativity, when light from an object in the distant universe travels close to a foreground source, it bends and amplifies (or magnifies) the light from the background object (Figure 3). This gravitational lensing effect facilitates the detection of faint objects not originally bright enough for detection.

However, it is important to know how large the gravitational amplification is in order to estimate the object's absolute luminosity, which relates to its stellar mass and formation history. Team member Nakahiro performed most of the amplification research as part of his university studies. Using observational data from the Subaru Telescope, the team used three quantities for estimating amplification to evaluate the mass of the foreground galaxy: 1) the distance from Earth to the background galaxy, 2) the distance between the foreground and background galaxies, and 3) the angular separation between the two galaxies.

Figure 3: Examples of gravitational lensing a) Schematic view of how gravitational lensing works. If there is not a foreground gravitational source, the black lines show how the light travels from the distant object and reaches Earth. If a gravitational source lies between Earth and the distant object, the red lines show how the light path bends and travels around the gravitational source. As a result, the distant object is amplified and another path of light reaches us. (Credit: Ehime University) b) Schematic view of LAE 221724+001716's configuration. Due to the gravitational lensing effect, light from the actual location of background galaxy 11.6 billion light years distant from Earth bends around the foreground galaxy that is 9.9 billion light years distant. As a result, the red-filled star (separated by 0.6 arcseconds from the foreground galaxy) shows the position at which the background galaxy was observed. (Credit: Ehime University)

The team found that the stellar mass of the foreground object was about a billion solar masses, which corresponds to only one percent of our Milky Way's mass (Figure 4).

The estimated stellar mass is rather small among the galaxies in the Universe, and its gravitational amplification is only about 20% at most. The foreground galaxy is still forming, and its stellar mass is increasing. The team concluded that the gravitational lensing effect from such young, forming galaxy does not significantly affect the luminosity of any background galaxies.

Figure 4: The relationship between the gravitational amplification factor and the stellar mass of the foreground galaxy. The red vertical line represents the upper limit of the estimated stellar mass, which provides an upper limit to the gravitational amplification. Credit: Ehime University

Nakahiro looks forward to future research in this area with great enthusiasm: "In this research, we have analyzed the gravitational amplification for only one object. Thus far, we have found similar objects in the literature, so I will evaluate the gravitational lens effects of these objects and tackle the challenging questions of our Universe."

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User comments : 101

As is common, the article confuses distance and time. The foreground galaxy is at z=1.76 which is a lookback time of 9.9 billion years. Its distance then was 5.75 Gly and is now 15.87 Gly.

The background galaxy is at z=3.1 which is a lookback time of 11.55 billion years. Its distance then was 5.22 Gly and is now 21.39 Gly.

It is interesting to note that the background galaxy was always farther away but due to the expansion between the two epochs, the light from the foreground galaxy was emitted at a greater distance from us.

As is common, the article confuses distance and time. The foreground galaxy is at z=1.76 which is a lookback time of 9.9 billion years. Its distance then was 5.75 Gly and is now 15.87 Gly.

The background galaxy is at z=3.1 which is a lookback time of 11.55 billion years. Its distance then was 5.22 Gly and is now 21.39 Gly.

Very true.

So I agree, but I don't think "the article" is confusing the distance/time willfully. I'm thinking it is a weak attempt by the people who write these "popular" summaries to explain the findings in the most basic terms possible. The folks in the Subaru Telescope (and all the other big telescopes) public relations/educational outreach depts try to gear these things for school age kids and completely "lay" adults.

So I agree, but I don't think "the article" is confusing the distance/time willfully. I'm thinking it is a weak attempt by the people who write these "popular" summaries to explain the findings in the most basic terms possible.

Undoubtedly, but they could as easily say the light "has taken 9.9 billion years to get here" and leave the question of distance out of the article entirely. IMHO, no information is better than disinformation. It's a tricky topic.

Very true, only slightly less counter-intuitive than quantum mechanics. It's too bad that they are limited in the space they can devote to their reporting,,,,

But how much more trouble would it be to provide a short list of links to more comprehensive explanations of the finer points? There is no shortage of good "popular" presentations on the internet that could be linked to.

the background galaxy was always farther away but due to the expansion between the two epochs, the light from the foreground galaxy was emitted at a greater distance from us

You got a point: It could falsify the whole expansion model of Universe just with trivial gravitational lensing phenomena: such a lensing couldn't happen, if the background galaxy wouldn't really this more distant one during most of time.

It's my opinion, that the reason so many new "theories" get presented on this type of forum is because so many people read a "popular" account of some aspects of physics, that has been so dumbed down that it gets many of the underlying principles wrong. They make it seem like it is easy to "know" without the nuances.

So ya end up with people who have only read a few "popular" books who think it is so easy, so simple, & that they deserve to be considered on par with the scientists who wrote the "popular" books.

Those people have acquired such a confidence in their "understanding", they don't feel at all constrained by the things they don't know, & don't understand. And come to places like this to to show off how well they "understand" the "deep" questions about the "reality" & the "universe".

The "lone" thinker making a substantial contribution to science are the thing of myth & legend. Through all history, they can be counted on one hand. If one has ever existed.

the background galaxy was always farther away but due to the expansion between the two epochs, the light from the foreground galaxy was emitted at a greater distance from us

You got a point: It could falsify the whole expansion model of Universe just with trivial gravitational lensing phenomena: such a lensing couldn't happen, if the background galaxy wouldn't really this more distant one during most of time.

Zeph, I realize that it is a counter-intuitive aspect of the standard cosmological model, but it doesn't falsify the expansion, it validates it. Without the expansion, what we see couldn't have taken place.

Very true, only slightly less counter-intuitive than quantum mechanics. It's too bad that they are limited in the space they can devote to their reporting,,,,

But how much more trouble would it be to provide a short list of links to more comprehensive explanations of the finer points? There is no shortage of good "popular" presentations on the internet that could be linked to.

For that matter, Phys.org could put up a single page explaining the relationship with a simple diagram and just refer all such references to that. It wouldn't be hard to put that into a data pack for their contributors.

It's my opinion, that the reason so many new "theories" get presented on this type of forum is because so many people read a "popular" account of some aspects of physics, that has been so dumbed down that it gets many of the underlying principles wrong. They make it seem like it is easy to "know" without the nuances.

That is so true. Again, if they just linked the original paper, people would at least see how much more there is behind the press releases. Unfortunately, it is often an amateur reporter with no scientific knowledge trying "tweak up" the official releases and posting them on sites set up solely to bring in advertising that gets the most views. The rule is the dumber the better, don't make the punters realise how little they really know.

Q-star, on another thread runrig described exactly what you are describing here Dunning-Kruger syndrome (or affect)(also called imposter syndrome or fraud symdrome). see: http://en.wikiped...syndrome

The issue with the article simplicity is really a tough nut to crack. If you make it too technical, eyes gloss over (lol great analogy btw) yet if you try for the biggest audience, the hard physics/math behind the seemingly simple article gets misinterpreted.

Still, as you both say, surely some imbedding of links to the more technical explanations can't be too hard. Time constraints perhaps?

the background galaxy was always farther away but due to the expansion between the two epochs, the light from the foreground galaxy was emitted at a greater distance from us

You got a point: It could falsify the whole expansion model ..

Nope. Let's see if a diagram will help. Below is as close as I cane get on this site, it's not to scale but the vertical axis is cosmic age while the horizontal scale is distance. The background galaxy "b" is always farther away but expansion means that it was closer to us when the universe was 2.25 billion years ago (i.e. 11.55 billion years ago) than the foreground galaxy "f" was when the universe was 3.9 billion years old. That's when the light from the distant galaxy passed it.

Q-star, on another thread runrig described exactly what you are describing here Dunning-Kruger syndrome

I saw that a while back. I've not written any popular science books, but I know several very popular science writers personally.

They routinely tell me that as much as they enjoy the money they earn from their writing, the greatest draw-back to it is this:

They receive hundreds of letters, emails, & even phone calls from people who read their book and "know" that they have hit upon a solution to some "dilemma" or "unsolved question" still plaguing "science".

They won't take NO for an answer. No matter how many times ya tell them: "That's already been thought of & discarded (by very many very smart people) by people who have spent their entire lives thinking about this subject". And they won't quit writing, emailing, & phoning. They just "know" they have pulled off an Einstein or Newton order insight.

That's funny Q-star! Stephen King was saying something very similar when he was talking about people who would come up to him and ask about the characters in his book The Stand as if they were real and alive and had continued to exist past the end of the book.

He got tired of patiently explaining that they were all figments of his imagination, and would oftimes tell them stuff like "oh Glen got his farm back" or some such. Too funny!

It is interesting to note that the background galaxy was always farther away but due to the expansion between the two epochs, the light from the foreground galaxy was emitted at a greater distance from us.

The lensing in this situation shouldn't be enough to make that true. The most extremely lensed light from the background would need to travel an extra distance that exceeds the distance between the two galaxies at the time the background light was emitted.

lookback time of 9.9 billion years. Its distance then was 5.75 Gly and is now 15.87 Gly

Something is wrong with that also. You're saying the universe expanded 10.12 billion ly in only 9.9 billion years. Superluminal expansion only happened in the inflation right after the BB.

It is interesting to note that the background galaxy was always farther away but due to the expansion between the two epochs, the light from the foreground galaxy was emitted at a greater distance from us.

The lensing in this situation shouldn't be enough to make that true.

The lensing is irrelevant in this case, it is simply the expansion between the two times.

lookback time of 9.9 billion years. Its distance then was 5.75 Gly and is now 15.87 Gly

Something is wrong with that also. You're saying the universe expanded 10.12 billion ly in only 9.9 billion years.

Remember the Hubble Law is a fractional change, the actual increase is proportional to the distance.

Superluminal expansion only happened in the inflation right after the BB.

The distance between us and an object seen at a redshift of 1.641 or higher was increasing by one light year per year when the light was emitted. We can see it because the Hubble Constant is always decreasing.

For the images of the two galaxies to be flip-flopped in age, they would have had to be expanding by more than one LY/Y relative to each other. Very distant objects expand at greater than one LY/Y relative to us, but both of the above galaxies are too close to eachother for that to happen relative to eachother. At short distance scales, the expansion is negligable.

Relative to eachother, they are receding away from us at basically the same rate; close enough for it to be called the same in this regard.

Without knowing how to book mark commentary thread I am force to make a non contributing comment. Why?Because this discourse means a 100% learning curve for me.Where I don't learn I don't rate or comment. Overlook this interjection in your discourse.

I learn the most when I see something someone says that 'smells funny' and then do massive google searches about any relavent terms. Some topics can take me on days of cross-referenced reading. Some of the people here seem to be saving time by simply making stuff up. I'm sure that's quicker than my way. lol.

Relative to each other, they are receding away from us at basically the same rate; close enough for it to be called the same in this regard.

Near enough. Consider a photon emitted from the more distant galaxy 11.55 billion years ago and moving towards us. At that time, the galaxy was 5.22 billion light years from us. 1.65 billion years later, it passed the foreground galaxy. However during that time, the distance between us and the foreground galaxy had expanded from less than 5.22 to 5.75 billion light years. Here's the diagram again with an asterisk indicating the photon. I've also added the 'f' and 'b' symbols on the first few lines. See if this makes it clearer:

@Fleetfoot,I'd like to commend ya on your artwork also. It it about the best I've seen anyone able to produce with the limited editor features here. It's too bad we couldn't be allowed to use the Greasemonkey editor on this site, the conversations would be so much more enjoyable and fluent.

@Zephyr,No Zeph, your pictures don't count, as much as I like them. They are indeed nice pictures, but hardy original like Fleetfoot's diagrams are.

Without knowing how to book mark commentary thread I am force to make a non contributing comment. Why?Because this discourse means a 100% learning curve for me.Where I don't learn I don't rate or comment. Overlook this interjection in your discourse.

No problem. I'm struggling with drawing in ASCII on the forum.

Here's the real chart showing black lines with "light cones" for the galaxies and the red line showing the path of the light that reaches us:

Has consensus on negligibility been reached? If the effect were negligible then what alternate interpretation of the data is there? Aberration?

Depends on the problem. Until two people agree on what is negligible, then they won't get to start working on the problem. The question must include an agreement of what is to be ignored. It's a scale/scope determined question. Depends on what ya are working on.

If ya read enough posts on this particular forum ya will find that some consider EVERYTHING known to be negligible.

Others consider everything BUT their pet crank theory to be negligible.

And sometimes the thing is negligible when it is in opposition to what they want ya to think. And other times it becomes of paramount, overarching and fundamental importance when they need it to convince they are "knowledgeable". (Meaning they will switch the laws of physics on and off in a whimsical manner.)

Near enough. Consider a photon emitted from the more distant galaxy 11.55 billion years ago and moving towards us. At that time, the galaxy was 5.22 billion light years from us

You are forgetting that the photons travelling through expanding space are being carried with that space, essentially slowing their speed relative to us now. The length of a lightyear is longer now than it was then. Expansion of the Universe isn't the same thing as objects spreading apart in a static Universe. The light from these two galaxies is not reaching us in reverse order. For that to be possible, you are violating the limit on the local speed of light between those two galaxies. There is no situation involving expansion that allows this. You cannot get light from one of them to pass the light from the other. Not in a Universe governed by a finite speed of light.

This is why people who equate time with distance are not incorrect. Expansion does not make this invalid.

(Meaning they will switch the laws of physics on and off in a whimsical manner.)

Yeah, like violating the limit of the speed of light to prove that light from a more distant object can pass light from a closer object?

lol

The ASCII diagram was a nice attempt, but it can't be correct. If you're going to allow light to pass other light, then you must toss out all of GR. To illustrate the error in that logic, consider light leaving from those two galaxies a billion years earlier or a billion years later than the exact moment he is incorrectly describing above. If you take it backwards a billion years, then events at the background location are ACTUALLY HAPPENING before the events in the foreground, not just appearing to happen before them. Time travel is not permitted, so quit it, or the GR police are gonna take away your physics license. :)

No, the speed of light hasn't changed and the year is a well-defined number of seconds.

From a local observer's point of view they will both measure exactly the same thing for distance and time. From an outside perspective, they are different. If you could hold two watches next to each other from each time/place they would run at different speeds and meter sticks would be different lengths.

Correct, and again I never suggested that it did. I think you have misunderstood what I said

Here's what you said:

the light from the foreground galaxy was emitted at a greater distance from us

The measure of distance has gotten longer. It's not more lightyears away from us; the lightyears are stretched. There's a profound difference. One is correct and the other isn't. They have significantly different meanings.

Here's a good analogy from the wiki page on metric expansion, though that page incorrectly describes objects as getting farther apart:

They mention that if you have tape measure between the two objects, you would see the marks on the tape measure spread apart. The tape measure would still reach from one object to the other without having to roll out any more tape. Light would still take the same amount of time to cross the length of the tape measure, from the point of view of the people at each level of expansion. So, it's actually not true when you claim that the objects are farther apart. They would still be the same number of lightyears apart at both times. The tape measure would still read the same number of inches.

This is what relativistic expansion of space-time means. Your mistake is that you are trying to force Euclidean geometry into a non-Euclidean reality.

So, it's actually not true when you claim that the objects are farther apart. They would still be the same number of lightyears apart at both times. The tape measure would still read the same number of inches.

I think that is not correct. The space is expanding. So two objects will be farther apart. If the space is expanding equally in all parts of the universe, then the distance between A B & C will maintain a constant ratio, this is what Hubble's constant tells us. It's a ratio of Velocity/Distance. Of course the light travel distances are increasing. That's the entire premise and foundation of the Standard Cosmological Model.

We observe it directly in redshift. Look-back time only relates the position of the light source when it emitted the light we see, to the actual position of the same light source is at now.

Here's a good analogy from the wiki page on metric expansion, though that page incorrectly describes objects as getting farther apart:

They mention that if you have tape measure between the two objects, you would see the marks on the tape measure spread apart. The tape measure would still reach from one object to the other without having to roll out any more tape.

Here is what is said on the Wikipedia page:

"if it were possible to place a tape measure between even stationary objects, one would observe the scale of the tape measure changing to show more distance between them."

That is exactly opposite of what you said. The explanation is that the material of the tape measure is held constant by EM forces between the atoms so doesn't change. If one end is fixed to a galaxy at rest* in its local space, a distant galaxy which is also locally at rest will move along the scale, the numbers read off will change.

Watching a discussion between supporters of the Einsteinian church is entirely uninteresting, it's as if none of them understand any of it. "What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it." Richard Feynman

Correct, and again I never suggested that it did. I think you have misunderstood what I said

Here's what you said:

the light from the foreground galaxy was emitted at a greater distance from us

No, this is what I said:

It is interesting to note that the background galaxy was always farther away but due to the expansion between the two epochs, the light from the foreground galaxy was emitted at a greater distance from us.

Its distance then was 5.75 Gly and is now 15.87 Gly.

That's not how it works.

The foreground galaxy is at z=1.76 while the background galaxy is at z=3.1. Put those values into Ned Wright's Cosmolcalc, click "flat" and examine the "light travel time", "comoving radial distance" and "angular size distance", you'll see the values I posted:

I think that is not correct. The space is expanding. So two objects will be farther apart. If the space is expanding equally in all parts of the universe, then the distance between A B & C will maintain a constant ratio

That would be the case if only distance was increasing, but time is changing proportionally along with distance. If only distance was increasing, then it would be impossible to tell the difference between expansion and physical motion. The wiki page on metric expansion actually misses a couple of points. One of those is that if expansion continues, distant objects will red-shift out of view. This will be due to frequency of the light being stretched so far that the energy of individual photons falls below the planck energy and they essentially cease to exist. This is not the same as outrunning the visible threshold governed by the speed of light, which is an effect of accelerating expansion. Even decelerating expansion will lead to objects redshifting out.

Watching a discussion between supporters of the Einsteinian church is entirely uninteresting, ..

Then why comment?

The topic we are discussing is well defined by the Fiedmann Equations, putting it into non-mathematical language is less simple and, as with any scientific subject, sometimes people understand 90% but aren't clear on some details. This forum supports discussions of such topics.

Keep reading the thread if you want to learn about the subject, ignore it if not, it's your choice.

That is exactly opposite of what you said. The explanation is that the material of the tape measure is held constant by EM forces between the atoms so doesn't change. If one end is fixed to a galaxy at rest* in its local space, a distant galaxy which is also locally at rest will move along the scale, the numbers read off will change

Well, this is a little confusing because the tape measure is fictional. Any real object will not be stretched by expansion, but this is a fictional tape measure that is allowed to stretch as light (which is unbound) does. This fictional tape measure would still reach between the two expanding objects without needing any more tape, and the number of inches from end to end will remain the same.

The disconnect between what I'm saying and what you are saying is that you are using an over-simplified description of expansion designed for laypeople to understand it. The idea of time expanding defies simple explanation.

The topic we are discussing is well defined by the Fiedmann Equations, putting it into non-mathematical language is less simple and, as with any scientific subject, sometimes people understand 90% but aren't clear on some details. This forum supports discussions of such topics.

That's the main problem with the lay public. They don't understand that people who study such things, often agree on principles, but have different "verbal" presentations of the same phenomena.

It's why they demand a 100% precise answer, ie, "the universe is 13.82 Gyr old", but the other "book" says "the universe is 13.71 Gyr old" and the "article says "14 Gyr old",,, so this means these guys disagree on everything and can't agree on anything.

If ya don't have everyone agree that galaxy X is exactly 4.506 732 954 018 300 Gly away, then the science is flawed. The same people who use this to dispute the science, never offer any calculations to give us the "real" numbers, only wordy "intuitions".

The disconnect between what I'm saying and what you are saying is that you are using an over-simplified description of expansion designed for laypeople to understand it. The idea of time expanding defies simple explanation.

But the time is not "expanding", it is inextricably linked to spacetime, but has a minus input into Einstein's and Freidmann's field equations. R^2 = x^ plus y^2 plus z^2 minus t^2, in it's simplest form.

The tape measure does not "expand" with the spacetime. If ya use the same tape to measure the distance between A and B at one time, & measure the distance between A and be at a later time, with a tape of the same length, ya will in fact measure a greater distance.

I think what is confusing ya is the fact that the light cones of the different galaxies causes them to become observable at DIFFERENT times to an observer in a constant reference frame. We observe them at different positions & at different times. While their relative positions also change.

You are both trying to fit expansion into a Newtonian reference frame.

That is why, at medium ranges, it is similar to the Doppler Effect

That's an example of applying a Newtonian solution to the problem in stead of the proper GR solution. In the Newtonian math, you can't tell the difference between an expanding Universe and objects moving away from one another in the coordinate system. In reality, it is not the same at any scale, though the difference is very small at local scales.

As for the tape measure, with all due respect, you're both wrong. If the tape same tape measure actually showed different distances at two times, this is inertial expansion (motion) rather than relativistic expansion of space-time itself.

One problem with both your views of expansion with Newtonian interpretation of increasing distance is that it would violate conservation of energy in the vacuum. You can't really ignore GR, even though Newton is close on small scales.

You are both trying to fit expansion into a Newtonian reference frame.

No, you were right the previous time, we're assuming the universe is flat hence the space part is Euclidean even in GR. Note that is the implication of the WMAP and Planck results. We're not contemplating Newton at all.

As for the tape measure, with all due respect, you're both wrong.

We are discussing the standard concordance model.

One problem with both your views of expansion with Newtonian interpretation of increasing distance is that it would violate conservation of energy in the vacuum. You can't really ignore GR, even though Newton is close on small scales.

We are using GR in the form of the Friedmann Equations. Energy is conserved for matter hence the expansion reduces the energy density, Omega_matter. The energy density for radiation falls faster hence the early universe changed from radiation- to matter-dominated at around 48,000 years.

One problem with both your views of expansion with Newtonian interpretation of increasing distance is that it would violate conservation of energy in the vacuum. You can't really ignore GR, even though Newton is close on small scales.

I'm not ignoring GR, that is why we posit dark negative vacuum energy, so that energy is conserved. I think ya are trying to manipulate what I actually said into something I didn't.

Newton does not explain what we see on cosmological scales. His theory would have space as static, absolute & entirely independent of time. If ya would spend a little time reviewing how spacetime & world-line diagrams work ya would see that both Fleetfoot & I, are actually representing the result of General Relativity, not the results of Newton's mechanics.

In all of Einstein's, Friedmann's, et al field equations, space & time are not joined in a linear manner. Time is dependent on the spacial reference frame. This is what Fleet's original comment addresses.

Yeah, like violating the limit of the speed of light to prove that light from a more distant object can pass light from a closer object?

This seems to have gotten lost in the discussion, but I want to point out that this is not what I understood him to be saying.

I read it to be that the when light from the more distant object reached the closer object, from that point the light from the two objects travelled togeather, arriving here at the same time. SO although the light from both arrived togeather, the light from the more distant object began its journey first, and its arrival at the same momonet as the closer object was only coincident with the light from the closer, as the closer object's light was emitted at the moment the object was being passed by the earlier emitted light.

So it is not a case of one object's light catching up to the other's light.

I read it to be that the when light from the more distant object reached the closer object, from that point the light from the two objects travelled togeather, arriving here at the same time. SO although the light from both arrived togeather, the light from the more distant object began its journey first, and its arrival at the same momonet as the closer object was only coincident with the light from the closer, as the closer object's light was emitted at the moment the object was being passed by the earlier emitted light.

So it is not a case of one object's light catching up to the other's light.

That's absolutely right. It is a given that we are talking about the light we are seeing now. Light from the foreground galaxy emitted at the same time as the light we are now seeing from the background galaxy would have arrived here a long time ago.

I read it to be that the when light from the more distant object reached the closer object, from that point the light from the two objects travelled togeather, arriving here at the same time. SO although the light from both arrived togeather

and

That's absolutely right. It is a given that we are talking about the light we are seeing now

They are 1.7 BLY apart. It would have taken 1.7 billion years for light from one to reach the other, at which point their photons would travel together. You're claiming that the pair moved more than 1.7 BLY away from us in the time of 1.7 billion years or less. That would be superluminal expansion, which you agree did not happen once inflation ended.

You're claiming that the pair moved more than 1.7 BLY away from us in the time of 1.7 billion years or less. That would be superluminal expansion, which you agree did not happen once inflation ended.

I claimed nothing of the sort GS. Once the light left the emitting object, it travelled to us at ~186,000MPS until it hit a detector. In this case, we see the emitted light from the background object striking the detector at the same moment as the light from the foreground object because the light from the backgound object happened to be passing by the foreground object when it emitted its light, and therefore was travelling along with the light from the foreground object. It has nothing to do with the movement of the objects that emitted the light.

You almost seem to be saying the light should "tire" due to its having travelled a longer distance? Is that what you're saying?

Fleetfoot claimed that the background galaxy was closer at the time it emitted its light than the foreground galaxy was at the time it emitted its light, which we are seeing at the same time.

I was arguing against that because it isn't possible unless you break at least one rule of GR.

As for expansion being very different from saying that distances increased; Superluminal inflation of spacetime is one illustration of the difference. The speed of light was not violated during inflation because the light was carried along with the universe as it expanded. In that universe a lightyear would have been more compact compared to now, but light would still take a year, as measured on a clock with that rate of flow of time, to cover that smaller lightyear. Ouch, that make my brain hurt.

So all the intervening comments have me confused. Maybe someone could restate the problem and let us begin anew.

You got my stance already, didn't you? Space-time doesn't expand.

Your stance keep changing. During the last year alone ya have gone between an expanding aether to a steady aether in an expanding space to a expanding aether in a steady space to a fluctuating aether in an expanding and steady space.

Ya didn't need to point out that time doesn't expand for ya. That is well demonstrated by the way ya always come back (by a twisted convoluted route) to the same old aether, ad infinitum.

I would prefer that that didn't happen. You can check what I'm saying in standard text books, the problem may have been that I was unclear in what I was saying at the start.

They are 1.7 BLY apart. It would have taken 1.7 billion years for light from one to reach the other, at which point their photons would travel together. You're claiming that the pair moved more than 1.7 BLY away from us in the time of 1.7 billion years or less.

Yes, they moved 1.88 Gly and 2.53 Gly respectivly in 1.66 Ga.

Distance then = distance now / (1 z)

They were 1.35 Gly apart at z=3.1, 2.00 Gly at z=1.76 and are 5.53 Gly apart now.

The speed of the background galaxy was 1.666c at z=3.1, 1.554c now and for the foreground galaxy 1.057c at z=1.76, 1.153c now.

That would be superluminal expansion, which you agree did not happen once inflation ended.

So, what I read from this is - The Space part of Space-Time is expanding - but the time part isn't.

Yes, expanding means increasing as a function of time but time changing depending on time is meaningless, changing relative to what?

And v=HoD is not subject to it's own constant?

The Hubble "constant" by definition uses distances measured along a surface of constant cosmic age and the subscript '0' means now. That follows automatically from the Cosmological Principle but says nothing about its time variation.

We can't observe those distances since light isn't instantaneous, we can only observe the past. For a radiation or matter dominated universe, the value of the constant falls to zero as the inverse of time, with dark energy included, it falls to a positive constant value to produce a universe which is asymptotic to the deSitter model.

but time changing depending on time is meaningless, changing relative to what?

But the proponents of Big Bang model are often arguing with just the claim, that before existence of Universe the time doesn't existed. Not to say about explicit speculations, that the time disappears from our Universe at the distance. Of course in water surface analogy of AWT it's evident, that the space-dimensions are mixed with time dimensions at distance (the gradient of density at the water surface serves as the time dimension there)

The deSitter model of universe considers the general relativity solution for universe driven with cosmological constant. The geometry of Universe is inverted geometry of black hole in it. But the black hole is steady state artifact in general relativity. From where you got the time dependent evolution of Universe in it?

During the last year alone ya have gone between an expanding aether to a steady aether in an expanding space to a expanding aether..

In AWT model the aether isn't expanding or steady state - it's random. Inside of random universe the notion of space-time expansion changes with distance and it completely vanishes in the sufficiently distant perspective. It's geometric effect, which is furthermore observer dependent in similar way, like the observation of distant objects inside of fog. You would see, that these objects are covered in fog, whereas at your place everything is visible. But the distant observer would see you covered with fog instead. Analogously we are observing the Universe expanding in the past, but locally nothing apparently expands (Einstein paradox), which is inconsistent with omnipresent expansion of Big Bang model.

Wow, FF. That all took a bit (of time) to process. In summation, tho, I think you are saying that time is the one constant by which all other things are measured. Correct? Not drawing any oddball conclusions here, but that just makes me wonder why the rules of equivalence/balance wouldn't apply to time...

Yes, expanding means increasing as a function of time but time changing depending on time is meaningless, changing relative to what?

Okay, one more time. I think Whydening is on the right track, he's just not forcing the issue as I am.

I assume you understand how clocks in different gravitational fields will run at different rates, yes? The same is true of clocks in areas of space with different amounts of expansion. The change in the rate of time is proportional to the rate of change in distances. So, as length increases, time must speed up, otherwise you violate the constancy of the speed of light. This is not allowed. You cannot actually add lightyears between places unless you are physically moving them to a new coordinate in the coordinate system. When space expands it changes the clocks too. This is the same as the twins paradox. The expansion of space is a property of space as is the rate of flow of time. You cannot change one without the other in our Universe.

If you could get into a spaceship and travel to an area of space with less expansion, and then travel back to where you started, the clock on board your spaceship would not show as much time had passed as the clocks that remained at your starting point. This works exactly the same as traveling into a gravitational field. Clocks here on Earth run slower than clocks on board our GPS satellites. We don't talk about it much, but if you could compare the length of a meter between the surface of the Earth and orbit, you would see a difference in length directly proportional to the difference in rate of time. This is required to maintain the speed of light as a constant. There is no known situation where this rule is violated, including expansion of the Universe. Time and space are inseperable as they are different measures of the same thing (spacetime).

Okay, one more time. I think Whydening is on the right track, he's just not forcing the issue as I am.

No problem, I'm happy to chat with people who are genuinely interested in the subject.

I assume you understand how clocks in different gravitational fields will run at different rates, yes?

I am well aware of the phenomenon but you need to be careful, there is no absolute measure of time in relativity so you can only say that one clock runs slow relative to another. I think may be at the root of our difference in views, you seem to be thinking that one clock can "run slow" in isolation but that has no meaning in either SR or GR.

If you think of two clocks moving apart in Minkowski spacetime, the "time dilation" factor depends on the angle between their worldlines. Something similar happens in the Schwarzschild metric but it is more complex because the lower clock is being pushed away from the free-fall geodesic.

Draw a vertical line and put dots on it on every gridline to mark clock ticks of 1s. Then move the slider at the top to show how they are viewed by another observer. Put the first line back to vertical then add a horizontal line and again put tick marks along it denoting 1 light-second distance intervals. Move the slider and see what happens. Remember you are not changing anything about the times or distances, just viewing events from the point of view of a differently moving observer.

Can you see why the lines can never cross 45 degrees? That produces a "light cone". The triangles here show future light cones in the big bang model:

This is the same as the twins paradox. The expansion of space is a property of space as is the rate of flow of time. You cannot change one without the other in our Universe.

That's true, but the trick in the twins is breaking the symmetry. In the case of cosmological expansion, we see time "running more slowly" in a distant galaxy, but similarly a scientist in that galaxy would see us running slow. As you say, that is the same as the situation in the twins paradox before one accelerates to rejoin the other.

It is wrong to think of time for either twin as "running slow", their clocks are ticking at the standard rate but in slightly different directions, their worldlines are not parallel. The same is true for two galaxies far apart in expanding space.

I've written more than enough already, if that makes sense, I'll address your second post.

I am well aware of the phenomenon but you need to be careful, there is no absolute measure of time in relativity so you can only say that one clock runs slow relative to another. I think may be at the root of our difference in views, you seem to be thinking that one clock can "run slow" in isolation but that has no meaning in either SR or GR

Yes, that's very close to the reason we aren't agreeing here. I see where you are getting stuck; it's because you're only thinking in terms of observers in constant spacetime. Bear with me, and I'll try to think of a good way to explain why the situation of expansion is different from what you're thinking about.

You said something about how one clock by itself cannot see relativistic effects, and I know what you're trying to say there. However, you're overlooking how that single clock can be compared to itself at different levels of expansion. Without anything else changing about the clock, it will change speed due to expansion.

Of course, you would need a way to compare that clock to iteself at different times, like a time machine with a window or something, lol.

Anyway, assuming that you are following me: The concept of expansion causes the rate of flow of time to change for the entire Universe, just as if an observer in the Universe were seeing local relativistic effects. You are only thinking in terms of the doppler effect due to physical motion. This is only half correct. The other half of the effect of expansion is that clocks at that distant past time in history actually were running slower relative to a clock at that same location today.

Most of the motion of the Universe today is actually physical, inertial movement, but that wasn't the case in the early Universe, as we see when we look at very old/distant things.

Michelson–Morley type experiments have been repeated many times with steadily increasing sensitivity. These include experiments from 1902 to 1905, and a series of experiments in the 1920s. In addition, recent resonator experiments have confirmed the absence of any aether wind at the 10−17 level

You said something about how one clock by itself cannot see relativistic effects, and I know what you're trying to say there. However, you're overlooking how that single clock can be compared to itself at different levels of expansion. Without anything else changing about the clock, it will change speed due to expansion.

Lost me with this one GS. Can you restate?

I'll bet you get banned from a lot of forums. Try reading this:

Ha, yes he sure does. I believe he was even banned from here 3 or more times. Energizer bunnie has nothing on ol Zeph!

but that wasn't the case in the early Universe, as we see when we look at very old/distant things.

@GSwift7: Try to carefully explain, how the negative result of Michelson-Morley experiment falsifies the luminiferous model and we will see. A historical hint: the zero result of M-M experiment can be derived easily from Maxwell's equations, which were itself based on aether model. How is it possible, that the result predicted with Maxwell's theory falsifies its physical model?

If by 'constant' you mean not expanding, that is not correct. You can see from the graphic from Wright's tutorial that the galaxies are moving apart and BTW I'm considering co-moving galaxies, i.e. ones that are notionally 'at rest' in their local space with no inertial motion, only expansion affecting them. It's easier to discuss under those conditions.

You said something about how one clock by itself cannot see relativistic effects, and I know what you're trying to say there.

Not quite. What I said is that there is only one time dimension so it is impossible to define something called the "rate of time".

by addressing certain mathematical problems in the original formulation

...with introduction of aether:"The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighborhood of the electric or magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced"

Anyway, it's not the main source of the controversy connected with widespread interpretation of M-M experiments as an absence of luminiferous aether. It's just one of multiple paradoxes, which emerged there.

However, you're overlooking how that single clock can be compared to itself at different levels of expansion. Without anything else changing about the clock, it will change speed due to expansion.

The phrase "different levels of expansion" is unclear to me. I would take it to mean clocks at different places such as in a gravitationally bound cluster versus in a cosmological void at the same time but obviously a clock cannot be in two places at once.

Of course, you would need a way to compare that clock to iteself at different times, like a time machine with a window or something, lol.

Therein lies your problem, it is impossible to compare one clock with itself at another time. All you can do is compare a clock to some other non-changing rate at one time and later compare it to the same reference, but no such reference exists, the universe has a (- ) Reimann signature, there is no second time-like axis.

"The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighborhood of the electric or magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced"

Exactly, as the quote says it was based on electric and magnetic fields acting directly on charged particles with no mention of an aether.

Anyway, it's not the main source of the controversy connected with widespread interpretation of M-M experiments as an absence of luminiferous aether.

On that you are right, it's a common misunderstanding. The MMX only showed that an aether could not be Galilean Invariant which led on to Lorentz's versions, it was Eddington's experiment that made the aether superfluous.

Anyway, assuming that you are following me: The concept of expansion causes the rate of flow of time to change for the entire Universe, just as if an observer in the Universe were seeing local relativistic effects.

No, expansion is defined by the scale factor a(t) as a fractional change of distances as a _function_ of time. It is in that sense a parametric equation taking time as the independent variable.

You are only thinking in terms of the doppler effect due to physical motion.

No, I have been discussing only co-moving galaxies throughout. Sorry if that hasn't been clear, I took it for granted.

Most of the motion of the Universe today is actually physical, inertial movement, but that wasn't the case in the early Universe, as we see when we look at very old/distant things.

That is not correct if I understand what you mean. Inertial motion is fairly random but always a small fraction of the speed of light. Expansion is superluminal at large distances.

Not quite. What I said is that there is only one time dimension so it is impossible to define something called the "rate of time".

That's just semantics, but I guess it's technically a valid point. It would have been more correct for me to have said "scale of time". So, my previous statements would have read something like "The scale of time changes in proportion to the scale of distance, so that a lightyear remains a lightyear at any given time or place". Expansion doesn't actually add lightyears between objects. That is a misconception.

Not quite. What I said is that there is only one time dimension so it is impossible to define something called the "rate of time".

That's just semantics, but I guess it's technically a valid point. It would have been more correct for me to have said "scale of time".

No, that's still the same problem. There is no temporal ruler outside the universe against whose scale you can read off the ticks of a clock to define a rate for it. You still have a background understanding that is based on 'absolute time' and I am going to struggle to get you past that block unless you realise that that one sentence is the root of the whole problem.

Expansion doesn't actually add lightyears between objects. That is a misconception.

Yes it does. That's why supernovae light curves get stretched, the tail of the pulse has to travel over more metre sticks (or light years) than the start of the pulse. Look at how a(t) enters into the Friedmann Equations if you doubt that.

The phrase "different levels of expansion" is unclear to me. I would take it to mean clocks at different places such as in a gravitationally bound cluster versus in a cosmological void at the same time but obviously a clock cannot be in two places at once

No, the exact same place, at two different times, in a Universe that is either expanding or contracting. At these two different times, a clock at this location will be running at different rates due to expansion/contraction. As you point out, it's the scale of time that has changed, so the clock will still have 60 minutes on it.

The same thing happens with distance. A given bit of space at two different times, in an expanding or contracting universe, will have different amounts of expansion. If you could compare a single meter stick at this stationary location at two different times, the length of the meter stick will change. It will still read 100cm, but the scale of those cm will change in exact proportion to the clock.

No, that's still the same problem. There is no temporal ruler outside the universe against whose scale you can read off the ticks of a clock to define a rate for it

Ah, so you disagree with general relativity then. This is one of the basic consequences of GR. That's what I meant earlier when I said you are talking about a static Universe. If you don't accept that time changes with expansion, then you're missing half the point of expansion. Oh, and BTW, mass changes too. Expansion causes the exact same kinds of paradoxes as relativistic acceleration or gravity.

You cannot add a lightyear between two stationary objects. Expansion does not mean that you are adding lightyears.

Let's do an example: A beam of light takes 1 LY to travel through a bit of stationary space. If we take that same space and make it an expanding space, the beam of light will still take 1 LY to cover that same space, but the beam will be stretched to a longer wavelength when it reaches point B.

You referenced the Friedman equations, so maybe I sould try to explain the problem in those terms then. The Friedman equations treat distance at different times as though it is "proper distance". This simplifies the equations, and makes it easier to interpret certain types of results, though it is actually proper to use comoving coordinates and hence comoving distances. This is related to the scale factor in the friedman equations. In using the scale factor, they are fixing the scale of time at a given point in time. In a more thorough treatment, you would need to use an intergral scale factor of time over some interval of time. See the wiki pages on scale factor and comoving coordinate systems:

BTW, Natelo, my previous post was directed at Fleetfoot, but the two links should answer your questions:

It indeed changes, but how it could eliminate the expansion of space between objects?

See the link to comoving distances.

and

IMO the metric expansion of space-time is based just on the gradually increasing distance between objects - this is how the red shift is supposed to work in mainstream cosmology

No, this isn't what expansion of the Universe means in GR. This is a common misconception. Even Fleetfoot seems to be surprised by this, and he seems to be way more knowledgable than the average guy around here. In fact, even QStar doesn't seem to understand comoving coordinates.

How? Why? I presume, we are thinking in realm of classical general relativity in 4D space-time by now

Yes, we are talking about GR, since this is what the orignal article is about.

No, that's still the same problem. There is no temporal ruler outside the universe against whose scale you can read off the ticks of a clock to define a rate for it

Ah, so you disagree with general relativity then.

No, I accept relativity, I disagree with what you are saying because IMHO you have a distorted understanding of it. You've put up some good examples that we can work through to try to resolve our disagreement.

This is one of the basic consequences of GR. That's what I meant earlier when I said you are talking about a static Universe. If you don't accept that time changes with expansion, then you're missing half the point of expansion.

What I am pointing out is that the phrase "time changes" on its own is incomplete, you can only compare two times. That's why it is called "relativity".

Oh, and BTW, mass changes too.

Mass is invariant in relativity, it is the magnitude of the energy-momentum 4-vector but let's not get sidetracked yet.

The phrase "different levels of expansion" is unclear to me. I would take it to mean clocks at different places such as in a gravitationally bound cluster versus in a cosmological void at the same time but obviously a clock cannot be in two places at once

No, the exact same place, at two different times, in a Universe that is either expanding or contracting. At these two different times, a clock at this location will be running at different rates due to expansion/contraction. As you point out, it's the scale of time that has changed, so the clock will still have 60 minutes on it.

There is some confusion here, I didn't say it was "scale", you did, you said: "It would have been more correct for me to have said "scale of time"."

I replied "No, that's still the same problem. There is no temporal ruler outside the universe against whose scale you can read off the ticks of a clock to define a rate for it."

The same thing happens with distance. A given bit of space at two different times, in an expanding or contracting universe, will have different amounts of expansion. If you could compare a single meter stick at this stationary location at two different times, the length of the meter stick will change. It will still read 100cm, but the scale of those cm will change in exact proportion to the clock.

That is not correct. The length of the ruler is fixed by the EM forces between the atoms so is unaffected by expansion. That should be easy to realise if you think about it.

From that, you can then infer that clocks don't change because the speed of light doesn't change but that's a bit of a circular argument, how can we know the speed of light doesn't change without making a presumption about clocks, so I suggest we don't follow that route. Instead I'll address your comments on proper versus comoving distances.

Let's do an example: A beam of light takes 1 LY to travel through a bit of stationary space. If we take that same space and make it an expanding space, the beam of light will still take 1 LY to cover that same space, ..

No. The current rate of expansion is 1% roughly every 140 million years but let's use a faster toy figure, say 1% per month. To make it easy, first imagine the increase happens as a step at the end of each month. When the light first starts out it has 12 light months (LM) to go. After one month, the distance ahead is 11 LM while behind it is 1 LM. At that moment, sizes increase by 10% so now the distance to go is 11.11 LM while that covered is 1.01 LM.

Another month later and the values are 10.11 and 2.01. Those expand to give 10.2111 and 2.0301. If you do a spreadsheet to repeat that process, you will find that by the time the light reaches the destination, it will have taken 12.71 months and covered a distance of 13.52 light months.

... An observer using "proper distance" in stead of "comoving distance" would not see the homogenous Universe we observe. Proper distance is only an analytical tool, not real.

I want to reply to this but it's 1am and I have to work tomorrow so it'll be tomorrow afternoon (early finish on Friday). In the meantime, that is incorrect. Proper distance is measured along a surface of uniform cosmic age (see Ned Wright's description of Hubble Distance) while comoving distance is the real value divided by the relative scale factor. That means that in the real world, matter density falls with cosmic age while the amount of matter in a comoving volume is essentially constant. However, the universe is homogenous in both measures.

Let's do an example: A beam of light takes 1 LY to travel through a bit of stationary space. If we take that same space and make it an expanding space, the beam of light will still take 1 LY to cover that same space, ..

No. The current rate of expansion is 1% roughly every 140 million years but let's use a faster toy figure, say 1% per month. ..., you will find that by the time the light reaches the destination, it will have taken 12.71 months and covered a distance of 13.52 light months.

The proper distance between the source and us was 12 LM at the start but has expanded to 13.52 now. That's an increase by a factor of 12.7%. The scale factor at the time of emission was 1/1.127=0.8876.

Now consider if that object was a galaxy whose width we knew. Two photons setting out at the same time but from opposites sides of the galaxy arrive with a slight angle between them. Because the expansion is isotropic, the angle isn't affected by the expansion.

If the universe obeys Euclidean geometry, we can use that angle and the known width to find the distance but note that it will be the proper distance at the time of emission.

In fact it seems that the overall geometry is very close to flat as measured by WMAP and PLANCK.

If your interpretation were correct, the angular size distance would always increase for increasing redshift but that is not the case, beyond z=1.64 it starts to fall because objects were closer when the light was emitted. You can get an example of that by increasing the expansion in the toy model to 10% per month. After one month, the light has moved 1 LM but the remaining 11 LM expands to 12.1 LM hence it is farther from us.

It is the proper distance (as measured by angular size distance in a flat universe) which is 'real' and comoving distance which is just a mathematically useful concept.

My work does not entail astronomy or cosmology. Like others here, I follow with interest your discourse over subtle differences in views that represent invaluable learning. For example I did not understand Whydening's questions until G7 chose to represent Whydening's questions as an incentive to address the differences being discussed among yourselves arising from your research.Please do not begin anew. This intervening comment was not meant to disrupt or distract from the focus of your discourse.

Nor mine, it's just a hobby. However, I have always taken learning seriously and recently completed a Caltech course on cosmology so I generally know where I can speak with some confidence and when to keep quiet ;-)

Like others here, I follow with interest your discourse over subtle differences in views that represent invaluable learning.

Thanks, sometimes it can feel as though these discussions are nothing more than a two-way argument.

Please do not begin anew. This intervening comment was not meant to disrupt or distract from the focus of your discourse.

My last set of posts was a lot longer than I like but it was very hard to cut it down without losing the logical connections. GSwift7's suggestion of using a 1 light year segment was good but he seems to have dropped out. I hope that's because he now follows but in trying to achieve clarity, my style can come over as browbeating which I hate.

{q}One second is defined as 9,192,631,770 oscillations of a particular transition in the caesium atom.The "rate of time" could then be the number of cycles of that wave in the time taken for 9,192,631,770 oscillations of that wave, divided by 9,192,631,770. That's going to be one, always.

So... Which came first? The oscillations or the time to oscillate in? Or perhaps it is similar to gravity in that you do not see it (is not there?) without matter...

{q}One second is defined as 9,192,631,770 oscillations of a particular transition in the caesium atom.The "rate of time" could then be the number of cycles of that wave in the time taken for 9,192,631,770 oscillations of that wave, divided by 9,192,631,770. That's going to be one, always.

So... Which came first? The oscillations or the time to oscillate in? ...

The two are the same in physics, 'time' is a count of the oscillations. There is no other independent variable against which you can compare the rate of oscillation to define a rate.

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